Problem: Simplify the following expression and state the condition under which the simplification is valid. $p = \dfrac{-5n^2 + 35n + 40}{4n^2 - 4}$
Solution: First factor out the greatest common factors in the numerator and in the denominator. $ p = \dfrac {-5(n^2 - 7n - 8)} {4(n^2 - 1)} $ $ p = -\dfrac{5}{4} \cdot \dfrac{n^2 - 7n - 8}{n^2 - 1} $ Next factor the numerator and denominator. $ p = - \dfrac{5}{4} \cdot \dfrac{(n + 1)(n - 8)}{(n + 1)(n - 1)}$ Assuming $n \neq -1$ , we can cancel the $n + 1$ $ p = - \dfrac{5}{4} \cdot \dfrac{n - 8}{n - 1}$ Therefore: $ p = \dfrac{ -5(n - 8)}{ 4(n - 1)}$, $n \neq -1$